What is the formula for ADC Quantization Noise Voltage?

The ADC Quantization Noise Voltage formula is e(rms) = q / √12, q = FS / 2ᴺ, where e—RMS quantization noise voltage (V); FS—Full-scale input range (V); N—Resolution in bits.

What does e mean in the ADC Quantization Noise Voltage formula?

e is RMS quantization noise voltage (V).

ADC Quantization Noise Voltage

Q: How do you calculate ADC Quantization Noise Voltage?

Use the formula e(rms) = q / √12, q = FS / 2ᴺ. Rounding a continuous signal to discrete ADC codes introduces quantization error spread over one least-significant-bit step (q). Enter the values you know in the calculator above and it solves for the remaining variable.

e = (FS / 2ᴺ) / √12

Calculator

RMS Quantization Noise

Full-Scale Range

Resolution (bits)

Result

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Formula

e(rms) = q / √12, q = FS / 2ᴺ

Description

Rounding a continuous signal to discrete ADC codes introduces quantization error spread over one least-significant-bit step (q). Treated as uniform noise, its RMS value is the LSB size divided by √12. This is the fundamental noise floor of an ideal converter and the basis from which the familiar SNR = 6.02N + 1.76 dB result is derived.

Variables

e — RMS quantization noise voltage (V)
FS — Full-scale input range (V)
N — Resolution in bits

Practical Notes

The LSB voltage is q = FS/2ᴺ. Real converters add thermal and jitter noise on top, so their effective resolution (ENOB) is below N.

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